Question

The energy required to remove the electron from a singly ionized Helium atom is \[2.2\] times the energy required to remove an electron from Helium atom. The total energy required to ionize the Helium atom completely is:
A) \[20{\text{ eV}}\]
B) \[79{\text{ eV}}\]
C) \[109{\text{ eV}}\]
D) \[34{\text{ eV}}\]

Answer 1

Hint: Find out the correct choice from all the choices by using the context of the problem. Go through the concept of ionization of atoms and energy required to make the correct choice.
Energy required to remove the electron from the outermost shell is known as threshold energy for that atom.

Complete step by step answer:
Write the expression for the energy \[{E_1}\] required to remove \[{e^ - }\] from singly ionised helium atoms.
\[{E_1} = \dfrac{{13.6{Z^2}}}{{{n^2}}}\]
Substitute \[1\] for \[n\] and \[2\] for \[Z\]
\[\
  {E_1} = \dfrac{{13.6{{(2)}^2}}}{{{1^2}}} \\
   = 54.4{\text{ eV}} \\
\ \]

Calculate the \[{E_2}\] energy required to remove \[{e^ - }\] from He –atom. Understand that,
\[{E_1} = 2.2{E_2}\]
Rearrange for \[{E_2}\]
\[{E_2} = \dfrac{{{E_1}}}{{2.2}}\]
Substitute \[54.4{\text{ eV}}\] for \[{E_1}\]
\[\
  {E_2} = \dfrac{{54.4{\text{ eV}}}}{{2.2}} \\
   = 24.7{\text{ eV}} \\
\ \]

Understand that, total energy required to remove both e−'s from He-atom is written as,
\[E = {E_1} + {E_2}\]
Substitute \[54.4{\text{ eV}}\] for \[{E_1}\] and \[24.7{\text{ eV}}\] for \[{E_2}\]
\[\
  E = 24.7{\text{ eV}} + 54.4{\text{ eV}} \\
   = 79.1{\text{ eV}} \\
\ \]
Therefore the total energy required to ionise He-atom is \[79.1{\text{ eV}}\].

So, the correct answer is “Option B”.

Note:
Understand that, to completely ionize the helium atom, two electrons from the outermost shell need to be ejected. Sum of the energies required to remove both electrons from the helium atom represent the ionization energy. Expression for the energy required to remove electrons from a helium atom is used to calculate the energy required to remove the first electron. Energy required to remove the second electron is calculated by using the expression provided.